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• Locally compact Hausdorff implies completely regular
  Any locally compact Hausdorff space is completely regular. ... * Compact Hausdorff implies normal * Paracompact Hausdorff implies normal ... ...
  1 KB (171 words) - 22:58, 24 January 2012

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• Locally compact Hausdorff implies completely regular
  Any locally compact Hausdorff space is completely regular. ... * Compact Hausdorff implies normal * Paracompact Hausdorff implies normal ... ...
  1 KB (171 words) - 22:58, 24 January 2012
• Locally compact Hausdorff space
  A topological space is termed locally compact Hausdorff if it satisfies ... locally compact Hausdorff implies completely regular * Locally normal space ... ...
  840 bytes (93 words) - 19:48, 11 May 2008
• Paracompact Hausdorff space
  A topological space is termed paracompact Hausdorff if it satisfies ... # It is paracompact and Hausdorff # Given any open cover of the space ... ...
  4 KB (516 words) - 23:41, 4 January 2017
• Completely regular space
  A topological space is termed completely regular if it satisfies the ... locally compact || locally compact Hausdorff implies completely regular | ... ...
  5 KB (670 words) - 18:02, 27 January 2012
• Compact Hausdorff space
  An arbitrary product of compact Hausdorff spaces is compact Hausdorff ... A closed subset of a compact Hausdorff space is compact Hausdorff ... ...
  5 KB (645 words) - 22:41, 29 April 2022
• Normal Hausdorff implies Tychonoff
  Any normal space is a Tychonoff space, i.e., it is both a completely ... * Locally compact Hausdorff implies completely regular ===Converse=== ... ...
  1 KB (231 words) - 22:04, 27 January 2012
• Regular space
  A topological space is said to be regular if it satisfies the following ... ! No. !! Shorthand !! A topological space is said to be regular if ... ...
  7 KB (1,057 words) - 16:37, 28 January 2012
• Normal Hausdorff space
  ! No. !! Shorthand !! A topological space is said to be normal Hausdorff ... be replaced by the (a priori stronger) Hausdorff space assumption, without ... ...
  10 KB (1,398 words) - 22:01, 27 January 2012
• Importance of Hausdorffness
  why we can remain within the world of Hausdorff spaces for a number of ... ==Usefulness of the Hausdorff assumption== ===The ability to separate ... ...
  8 KB (1,265 words) - 19:47, 11 May 2008
• Compact Hausdorff implies normal
  Any compact Hausdorff space (a topological space that is both a compact ... * Paracompact Hausdorff space: paracompact Hausdorff implies normal ... ...
  5 KB (868 words) - 04:25, 30 January 2014
• Hausdorff space
  A topological space is said to be Hausdorff if it satisfies the following ... ! No. !! Shorthand !! A topological space is termed Hausdorff if ... ...
  13 KB (1,927 words) - 01:36, 5 January 2017
• Contractible space
  * Compact manifolds in dimension one or more, such as the circle, ... the line segment joining the points is completely inside the space. ... ...
  15 KB (2,146 words) - 22:57, 26 October 2023